Mathematical Sciences: Vortices in Algebraic and Symplectic Geometry

数学科学：代数和辛几何中的涡旋

• 批准号: 9303545
• 负责人: Steven Bradlow
• 金额: $ 4.02万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-06-01 至 1995-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9303545&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Vortices; Algebraic; Symplectic

This award supports research in the area of vortices in algebraic and symplectic geometry. It is based on earlier work by the investigator on vortices and stable holomorphic pairs. Vortices are minima of Yang-Mills-Higgs energy, and holomorphic pairs are holomorphic vector bundles with prescribed holomorphic sections. This research concerns new directions in the study of vortices and stable pairs and involves a generalization of the notion of a pair to that of a triple consisting of two holomorphic bundles together with a holomorphic bundle homomorphism. This will address the way in which objects can be obtained by a dimensional reduction of an equivariant stable bundle on the Cartesian product of the Riemann surface with the projective line. This award is in the general area of geometry and, in particular, in algebraic and symplectic geometry. This research will aid in our understanding of 4-dimensional manifolds and are central to the current research in 'gauge theory'. In lay terms, a 'manifold' plays the role of a surface.

该奖项支持在涡流领域的研究， 代数和辛几何。 它是基于早期的工作 研究涡旋和稳定的全纯偶的人。 涡旋是杨-米尔斯-希格斯能量的最小值， 对是全纯向量丛，具有规定的全纯 路段 这项研究涉及到研究的新方向， 涡和稳定的对，并涉及一个推广的 一对的概念到由两个组成的三元组的概念 全纯丛与全纯丛 同态 这将解决对象可以被 通过等变稳定的降维获得 在黎曼曲面的笛卡尔积上的丛， 投影线 这个奖项是在一般领域的几何，并在 特别是在代数和辛几何中。 本研究 将有助于我们理解四维流形， 当前研究的核心是“规范理论”。 在外行看来， "歧管“起到表面的作用。